efficient resource allocation for wireless multicast

1
efficient resource allocation for wireless
multicast

• De-Nian Young
• Ming-Syan Chen
• IEEE Transactions on Mobile Computing
• Slide content thanks in part to Yu-Hsun Chen,
  University of Taiwan

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Introduction

• Environment
• Wireless Multicast Networks
• Heterogeneous Devices and Cells
• Differing Costs per Cell
• Problem
• Given a Heterogeneous Network, Select the Lowest
  Cost Distribution Tree
• NOT STATED From the perspective of the network
  owner!

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Heterogeneous Environment
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Heterogeneous Network Theory

• Current mobile devices have multiple radios
• Can connect via
• Wi-Fi
• WiMax
• 3G
• EVDO
• Satellite
• Bluetooth (presumably tethered)

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Heterogeneous Network Theory contd

• Devices (mobile hosts) can choose which radio and
  which cell to connect to with that radio to get
  Mobile-IP multicast messages
• Different cells have different costs to both the
  distributor and mobile host
• By aggregating individual mobile hosts
  appropriately, the provider can reduce overall
  bandwidth costs for multicasting

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Concept Shortest Path Tree

• SPT
• Easy to build (Dijkstras algorithm)
• Not necessarily the most efficient in bandwidth
  usage

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Concept Minimum Cost Tree

• MCT
• Finds the minimum cost tree for a given graph
• NP-hard!

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Cell and Technology Selection Problem

• CTSP reformulation of Minimum Cost tree
  problem.
• Contributions
• For each technology Clusters mobile hosts and
  reduces the number of cells in the SPT.
• Takes into account bandwidth costs of links
  (weighted edges).
• Transparent to the IP multicast protocols
• Supports dynamic group membership (necessary for
  moving hosts)

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CTSP Assumptions

• All wireless cells are multicast capable
• Paths from root to host are pre-given by the
  multicast protocol
• Unwritten
• The root bears the bandwidth costs (questionable
  in practice)
• The individual nodes have multiple cells and
  multiple technologies to choose from (again,
  questionable AND irrelevant different
  technologies are the same as different cells when
  weighted!)

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Notation
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Integer Linear Programming
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ILP, contd

• Objective function for ILP formulation
• Constraints

Minimum bandwidth
Each mobile host selects one cell
A cell is used in the shortest path tree if it
is selected by any mobile host
A link is used in the shortest path tree if it
is on the path from any selected cell to the
root of the tree
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LAGRANGE Algorithm

• Modification to ILP
• Relaxes a constraint to reduce complexity
  (relaxation just sound better than cheating by
  approximation)

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LAGRANGE

• Relax the second constraint ( ) in
  the ILP
• New objective function
• Lagrange multiplier the cost of cell c
  for mobile host m
• Constraints

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LAGRANGE - Properties

• Properties
• For any feasible solution to the LRP that
  contradicts the relaxed constraints (
  ), the objective value is larger
• Any feasible solution to CTSP is a feasible
  solution to the LRP
• When adopting the optimal solution to CTSP, the
  objective value of LRP lt the objective
  value of CTSP
• The objective value of the optimal solution to
  the LRP provides a lower bound to CTSP

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LAGRANGE Subproblem 1

• Objective function of the subproblem 1
• Constraint
• The runtime is
• The cost for cell c is stored in each
  mobile host m

Find the cell with the minimum cost for each
mobile host m
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LAGRANGE Subproblem 2

• Objective Function
• Constraint

Minimize the net cost of all selected Cells in
the shortest path tree
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LAGRANGE Subproblem 2, contd

• To find the minimum net cost of the whole
  shortest path tree, we consider each link in the
  bottom-up manner
• the minimum net cost of the subtree that
  includes link and the subtree rooted at v

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LAGRANGE Subproblem 2, contd

• All cells in the subtree corresponding to a link
  are not selected if net cost is not
  negative
• Each candidate cell c is selected in the second
  subproblem if the net cost of every link
  in the shortest path from c to the root of
  the tree is negative

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LAGRANGE - Iterations

• The selected cells may not be feasible to CTSP
• Each mobile host is not guaranteed to be covered
  by a cell that is selected in the second
  subproblem
• Each member m in the LAGRANGE algorithm selects
  the cell c according to the cost in the
  first subproblem
• Adjust the cost iteratively with the subgradient
  algorithm and the solutions to the two
  subproblems of the LRP
• the objective function of the LRP
• The subgradient of the LRP

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LAGRANGE - Iterations

• The subgradient indicates the direction of
  adjusting to find the better feasible
  solution to CTSP
• increase
• decrease
• The second subproblem tends to
• Select the cells cover more mobile hosts to save
  wireless bandwidth
• Select the cells such that the shortest path from
  the cells to the root share more common wireline
  links

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Protocol Design

• A distributed protocol based on the LAGRANGE
  algorithm
• Data tree the shortest path tree for data
  delivery
• Control tree to solve the second subproblem in a
  distributed manner
• Initially the control tree spans every candidate
  cell
• Incrementally prune the control tree to reduce
  the protocol overhead
• Each router and base station in the control tree
  maintains a node agent and cell agent

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State

• Each node agent stores the following states
• Multicast group address
• The address of the parent node agent in the
  control tree
• The bandwidth cost of the link with the parent
  node agent
• The address of the child agent and a Join timer
• Each cell agent stores the following states
• The bandwidth cost of the cell
• Control Flag (whether the cell is selected)
• Data Flag (whether the base station is in the
  data tree)
• The address of the mobile host
• The cost of the cell for the mobile host
  (Lagrange multiplier)
• Join timer

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Control Messages

• Join
• Mobile hosts or node agents send Join to join the
  control tree
• Join_Ack
• Confirm the Join message
• Contain the Data Flag and the cost of the cell
  for the mobile host (sent by cell agent)
• Leave
• Sent by mobile hosts, cell agents, and node
  agents
• Request, Reply, and Inform
• Update the cost of each cell in a distributed
  manner

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Operations 1

• Join a multicast group
• Mobile host sends a Join message to the cell
  agent of each cell that covers the mobile host
• Handover to a new cell
• Mobile host sends a Join message to the new cell
  and a Leave message to the original cell
• Leave the multicast group
• Mobile host sends a Leave message to cell agent

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Operations 2

• Update the cost of each cell
• Root periodically sends a Request message
• Cell agent first calculates the net cost ? Set
  Control Flag ? send Reply message
• Node agent first calculates the net cost ?
• send Reply message to parent node agent
• If net cost 0, send Inform
• message to child node agent

Inform
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Operations 3

• Prune the control tree
• Cell agent or node agent obtains a zero net cost
  for a period of time
• A node agent leaves the control tree if it
  receives a Leave message from every child agent

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Results for Small Wireless Networks

• 25 km 25 km, 36 hexagon cells

Simulation results of small wireless
networks. (a) total bandwidth cost. (b) number of
cells in the tree.
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Results for Large Wireless Networks 1
Simulation results of large wireless networks (a)
original scenario (b) larger transmission range
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Results for Large Wireless Networks 2
Simulation results of large wireless
networks. (c) (d) zero bandwidth cost for each
link.
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Transient Behavior of the LAGRANGE Algorithm
Transient behavior of the LAGRANGE algorithm with
different mobility (a) Probability 0 percent
(b) 0.1 percent (c) 0.5 percent (d) 2 percent
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Conclusions

• LAGRANGE provides a solution to the lowest cost
  spanning tree problem
• The solution uses an iterative approximation
  approach
• Problems
• It really doesnt address heterogeneous networks
• The comparison choices in the experimental
  results are dubious
• It assumes the root bears the cost (not likely)
  or that it can be somehow transferred to the
  client

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Details of the algorithm 1
assign a unit cost to each cell for each member
find the solution to the first subproblem
every cell is selected in the first subproblem
initial topology
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Details of the algorithm 2
find the solution to the second subproblem
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Details of the algorithm 3
1(-1)0
no cell is selected in the second subproblem
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Details of the algorithm 4
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Details of the algorithm 5
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Details of the algorithm 6
H3 handovers from C4 to C2 H5 moves out C4 H7
leaves the multicast group
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Details of the algorithm 7
adjustment after the mobility